Question

find the cost of plastering the curved surface of a well 8 m deep and 21 m in diameter at the rate of rupees 20 per m²​

Answer 1

Given : The Diameter of the well is 21 cm and its depth is 8 cm .Rate of plastering is Rs.20 per m² .

To Find : Find the Cost of Plastering

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SolutioN :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Curved \; Surface \; Area = 2 \pi rh }}}}}$

Where :

• $\sf{ \pi = \dfrac{22}{7} }$

• r = Radius
• h = Height

$\maltese$ Calculating the CSA of well :

$\begin{gathered} \qquad \; \; \longrightarrow \; \sf { CSA = 2 \pi rh } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \sf { CSA = 2 \times \dfrac{22}{ \cancel7} \times \dfrac{ \cancel{21} }{2} \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \sf { CSA = 2 \times 22 \times \dfrac{3}{2} \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \sf { CSA = \cancel2 \times 22 \times \dfrac{3}{ \cancel2} \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \sf { CSA = 22 \times 3 \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \sf { CSA = 66 \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; {\underline{\boxed{\purple{\sf{ Curved \; Surface \; Area = 528 \; {m}^{2} }}}}} \; {\pink{\bigstar}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Cost of Plastering :

$\begin{gathered} \qquad \; \leadsto \; \; \sf { Cost = CSA \times Rate } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \leadsto \; \; \sf { Cost = 528 \times 20 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \leadsto \; {\underline{\boxed{\color{darkblue}{\sf{ Cost \; of \; Plastering = Rs. \; 5280 }}}}} \; {\red{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Cost of Plastering is Rs.5280 .

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Answer 2

$\bold{ANSWER≈}$

Since the well is cylindrical its curved surface area with base radius 'r' and height 'h' is 2πrh.

Diameter of the well, d = 3.5 m

Radius of the well, r = d/2 = 3.5/2 m = 1.75 m

Depth of the well, h = 10 m

i) The inner curved surface area of the well = 2πrh

= 2 × 22/7 × 1.75 m × 10 m

= 110 m²

ii) We can calculate the cost of plastering by multiplying the curved surface area of the well and the rate of plastering per square meter.

Cost of plastering the curved surface area at ₹ 40 per m2 = 110 × 40 = ₹ 4400

Thus, the inner curved surface area is 110 m² and the cost of plastering the circular well is ₹ 4400.